Devlin's
Angle

April 2002

Mathematics and Homeland Security

During the 1950s and 60s, the United States poured
millions of dollars into mathematics research as
part of the national effort to fight (or at least
to avoid losing) the Cold War. This came on the
heels of the crucial, and successful, role
mathematicians played during the Second World War.

Today the United States finds itself in a new
war, an international War on Terror. Since the
opening salvo in this new war was launched on the
continental USA, and because the next attack could
likewise take place in America, Homeland Security
is a high priority in the new struggle. And once
again, the US is looking to the mathematical
community to assist in the conflict.

As part of the mathematical profession's initial
response, later this month (on April 26-27) the
National Academies' Board on Mathematical Sciences
and their Applications (BMSA) is holding a two-day,
invitational workshop on The Mathematical
Sciences' Role in Homeland Security, hosted by
the National Research Council in Washington, D.C.
The aim is to bring together leading experts in
the various areas of mathematics that are likely
to be required in fighting international terrorist
organizations, with a view to setting a national
research agenda to aid the country in combating
this new kind of warfare.

Mixing with mathematicians from universities,
industry, and national laboratories at the workshop
will be senior representatives from the Defense
Advanced Research Projects Agency (DARPA), the
National Security Agency (NSA), the Centers for
Disease Control and Prevention (CDCP), the
Directorate of Defense Research and Engineering,
and of course the Office of Homeland Security.

The topics to be discussed fall into five general
(and overlapping) areas: Data Mining and Pattern
Recognition, Detection and Epidemiology of
BioTerrorist Attacks, Voice and Image Recognition,
Communications and Computer Security, and Data
Integration/Fusion.

Many if not all of these areas are unfamiliar
to most mathematicians, and they are quite
different from the kinds of mathematics that
were required to fight wars in the past, hot or
cold. Statistical and computational techniques
figure heavily in this new kind of strategic
mathematics.

Data Mining and Pattern Recognition looks
for ways to discover patterns, structure, or
associations in large bodies of empirical data,
such as financial or travel records. Much of the
early research in this area was developed for
industrial and commercial purposes, for instance,
by banks to detect credit card fraud, by telephone
companies to spot unauthorized use of the phone
system, and by supermarket chains to identify
purchasing patterns. (Why do you think they
have those electronically readable "store
membership cards"?) The relevance of this area
of research to homeland security is obvious.

Detection and Epidemiology of BioTerrorist
Attacks involves a number of lines of
mathematical research. The development of
mathematical models of how diseases spread is
perhaps one of the most well known examples -
well known in part because simple scenarios
form standard examples in calculus classes. In
fact, within days of the September 11 attacks
on the World Trade Center towers and the Pentagon,
researchers at Los Alamos National Laboratories
had taken a mathematical model of traffic flow
they had been developing and applied it to
predict the likely spread of disease following
a possible bioterrorist attack. There is
significant scope for further research into
the mathematics of how biological and chemical
agents spread.

Another area where mathematics will be important
in countering a biological or chemical attack is
in early detection that such an attack has in
fact taken place. In the early stages, it can be
hard to differentiate between a malicious attack
with a dangerous weapon and a naturally occurring
outbreak of a common agent. The available data is
almost always noisy, creating a need for better
techniques to integrate and fuse data to identify
patterns, determine sources, increase confidence,
and predict the spread of infectious or chemical
agents, in order that the available counter agents
of containment methods may be brought to bear in
the most timely and efficient fashion. As the
science of patterns, mathematics may turn out to
be one of the main weapons in the nation's arsenal
in fighting this new kind of war.

Voice and image recognition: Today's
terrorists operate globally, maintaining contact
by telephone and the Internet. Identifying the
occasional key telephone conversation among the
millions that take place daily can only be done
(if it can be done at all) using sophisticated
automation, with monitoring systems that are able
to break down voices and words into digital
patterns that can be scanned for keywords. This
requires the development of new algorithms to
monitor communications channels in real time to
provide the nation's defense authorities with
early warnings of a potential threat. Similarly,
methods need to be developed for the automated
screening of images sent over the Internet, to
look for messages embedded in pictures
(steganography), a technique believed to have
been used by the September 11 terrorists.

New and more sophisticated mathematical techniques
for image processing and recognition will also be
required to identify potential terrorists involved
in suspicious activities and to improve screening
at airports and other checkpoints.

Communications and Computer Security: Most
mathematicians are familiar with the basics of
cryptography. This, after all, is one of the areas
where mathematics played a major role in the Second
World War. But with secure encryption systems now
widely available to security forces and terrorist
alike, the focus has shifted elsewhere, to the
overall integrity of communication and computer
systems. A secure cryptosystem becomes worthless
if an enemy can break into your computer or
disrupt the network. There is thus a pressing need
for taking a broad look at computers and computer
networks to examine their vulnerabilities and
develop ways to defend them, including early
detection of an attack. New methods for analyzing
Internet traffic are likely to be important in
this new area of cyber warfare.

Data Integration/Fusion is the process of
synthesizing information from diverse sources in
order to make prudent decisions. At present there
is little by way of a reliable mathematical
framework to support this kind of activity.
Current practitioners make largely ad hoc use of
statistics, probability, decision theory, graph
theory, and tools from artificial intelligence and
expert systems design. The relevant parts of these
disciplines need to be merged into at least a
compatible toolkit, if not a coherent theory. I
know first hand from my own attempts over the past
twenty years to come to grips with information
representation that there are enormous theoretical
challenges to be overcome in order to make
progress in this now crucial area.

The Washington workshop is not going to provide
answers to any of the pressing questions
that need to be answered. That is not the purpose.
As with the war on terrorism itself, we are in
the early days of what will certainly be a long
haul. The workshop is intended merely to draw up
a roadmap of where we want to go and how we might
get there.

Much of the work that has to be done will not be
"hard, elegant" mathematics of the kind that many
mathematicians (myself included) view as a thing
of beauty. (Although history tells us that there
is a high probability that this effort will lead
to such mathematics as an unintended side-effect.)
Consequently, there are likely to be few public
rewards or accolades for those who choose to
engage in such projects. But it is work that can
only be done by mathematicians. Such was the case
with the part played by mathematicians in previous
conflicts. Now, as then, I doubt there will be any
shortage of willing volunteers.